Weighted Bergman Spaces Induced by Rapidly Increasing Weights

Released on by Jose Angel Pelaez
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  • Weighted Bergman Spaces Induced by Rapidly Increasing Weights Book Detail

  • Author : Jose Angel Pelaez
  • Release Date : 2014-01-08
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 136
  • ISBN 13 : 0821888021
  • File Size : 23,23 MB
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Weighted Bergman Spaces Induced by Rapidly Increasing Weights by Jose Angel Pelaez PDF Summary

Book Description: This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.

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